NPMLEmix-package: Likelihood based inference in mixture models and multiple...
In NPMLEmix: Two-Groups Mixture Model with Covariates

Description Details Functions References

The NPMLEmix-package fits nonparametric Gaussian location mixture models for z-scores arising out of several hypotheses, while taking into account any available covariate information. It also provides three important functions: marg1(), marg2() (both based on marginal likelihoods), npmleEM() (based on joint data likelihood) for inference in multiple testing.

(Y_1,X_1),… ,(X_n,Y_n) are i.i.d. samples drawn from the model,

Y|X=x\sim (1-π^*(x))φ(y)+π^*(x)\underbrace{\int_{θ}φ(y-θ)\,dG(θ)}_{φ_1(y)}, \qquad X\sim m_X(\cdot)

where π^*(\cdot) represents the logistic link function, φ(\cdot) is the standard Gaussian density and G(\cdot) is some unknown probability measure on the real line. Usually, π^*(\cdot) is referred to as the signal proportion, φ_1(\cdot) is called the signal density and G(\cdot) is called mixing distribution. The i^{th} local false discovery rate is then defined as

lfdr_i=\frac{(1-π^*(X_i))φ_0(Y_i)}{(1-π^*(X_i))φ_0(Y_i)+π^*(X_i)φ_1(Y_i)}

All the principal functions estimate the unknown parameters - π^*(\cdot) and φ_1(\cdot), and consequently the lfdr_i's. The optimization algorithms use quasi-Newton routines such as the BFGS (Broyden-Fletcher-Goldfarb-Shanno) algorithm and the separable convex optimization routine available in the Rmosek optimization suite. The principal functions accept a vector of z-scores (Y)'s and a covariate matrix X in their list of arguments. Read the documentations for each function to check whether or not to add a column of 1's to X matrix.

The principal functions in the NPMLEmix-package: marg1(), marg2(), npmleEM().

Deb, N., Saha, S., Guntuboyina, A. and Sen, B., 2018. Two-component Mixture Model in the Presence of Covariates. arXiv preprint arXiv:1810.07897.

Scott, J.G., Kelly, R.C., Smith, M.A., Zhou, P. and Kass, R.E., 2015. False discovery rate regression: an application to neural synchrony detection in primary visual cortex. Journal of the American Statistical Association, 110(510), pp.459-471.

Efron, B., 2005. Local false discovery rates.

Koenker, R. and Mizera, I., 2014. Convex optimization in R. Journal of Statistical Software, 60(5), pp.1-23.

NPMLEmix documentation built on Dec. 6, 2020, 9:06 a.m.